In typical robotics pipelines, the measurement likelihood is constructed using custom metrics, based on models of the sensors in question. Inevitably, some elements of the model are imprecise. For example, covariances in visual odometry models are typically tuned manually since closed-form solutions are difficult to obtain. Additionally, the Gaussian assumption (e.g., in an EKF) is clearly inappropriate for the task of global localization, as evidenced by the prevalence of Monte Carlo based solutions [1]}.
